Question

1. identify any restrictions on the variable

\\(\frac{x^2 + 13x + 40}{x^2 - 2x - 35}\\)
\\(\circ\\) \\(x \
eq -8\\) or \\(x \
eq -5\\)
\\(\circ\\) \\(x \
eq -8\\) or \\(x \
eq 7\\)
\\(\circ\\) \\(x \
eq -7\\) or \\(x \
eq 5\\)
\\(\circ\\) \\(x \
eq -5\\) or \\(x \
eq 7\\)

Explanation:

Step1: Set denominator to zero

$x^2 - 2x - 35 = 0$

Step2: Factor denominator

$(x - 7)(x + 5) = 0$

Step3: Solve for x

$x = 7$ or $x = -5$

Step4: State restrictions

$x
eq -5$ and $x
eq 7$

Answer:

$x
eq -5$ or $x
eq 7$